A332126 - OEIS

%I #14 Jul 13 2024 17:30:25

%S 6,262,22622,2226222,222262222,22222622222,2222226222222,

%T 222222262222222,22222222622222222,2222222226222222222,

%U 222222222262222222222,22222222222622222222222,2222222222226222222222222,222222222222262222222222222,22222222222222622222222222222,2222222222222226222222222222222

%N a(n) = 2*(10^(2n+1)-1)/9 + 4*10^n.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).

%F a(n) = 2*A138148(n) + 6*10^n = A002276(2n+1) + 4*10^n = 2*A332113(n).

%F G.f.: (6 - 404*x + 200*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).

%F a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

%F E.g.f.: 2*exp(x)*(10*exp(99*x) + 18*exp(9*x) - 1)/9. - _Stefano Spezia_, Jul 13 2024

%p A332126 := n -> 2*(10^(2*n+1)-1)/9+4*10^n;

%t Array[2 (10^(2 # + 1)-1)/9 + 4*10^# &, 15, 0]

%t Table[FromDigits[Join[PadRight[{},n,2],{6},PadRight[{},n,2]]],{n,0,20}] (* or *) LinearRecurrence[{111,-1110,1000},{6,262,22622},20] (* _Harvey P. Dale_, Oct 17 2021 *)

%o (PARI) apply( {A332126(n)=10^(n*2+1)\9*2+4*10^n}, [0..15])

%o (Python) def A332126(n): return 10**(n*2+1)//9*2+4*10**n

%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).

%Y Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

%Y Cf. A332116 .. A332196 (variants with different repeated digit 1, ..., 9).

%Y Cf. A332120 .. A332129 (variants with different middle digit 0, ..., 9).

%K nonn,base,easy

%O 0,1

%A _M. F. Hasler_, Feb 09 2020